Empirical Likelihood Ratio Tests for Two Sample Comparison Under Current Status Data PDF Download
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Author: 侯科宇
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Category :
Languages : en
Pages :
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Author: 侯科宇
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: 許玳瑜
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Category :
Languages : en
Pages :
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Author: 洪于景
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Category :
Languages : en
Pages :
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Author: Paul Shen
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 19
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Book Description
In this thesis, we investigate the problem of testing constant variance. It is an important problem in the field of statistical influence where many methods require the assumption of constant variance. The question of constant variance has to be settled in order to perform a significance test through a Student t-Test or an F-test. Two of most popular tests of constant variance in applications are the classic F-test and the Modified Levene's Test. The former is a ratio of two sample variances. Its performance is found to be very sensitive with the normality assumption. The latter Modified Levene's Test can be viewed as a result of the estimation method through the absolute deviation from the median. Its performance is also dependent upon the distribution shapes to some extent, though not as much as the F-test. We propose an innovative test constructed by the empirical likelihood method through the moment estimation equations appearing in the Modified Levene's Test. The new empirical likelihood ratio test is a nonparametric test and retains the principle of maximum likelihood. As a result, it can be an appropriate alternative to the two traditional tests in applications when underlying populations are skewed. To be specific, the empirical likelihood ratio test of constant variance uses the optimal weights in summing the absolute deviations of observations from the median values, while the Modified Levene's test uses the simple averages. It is thus desired that the empirical likelihood ratio test is more powerful than the Modified Levene's test. Meanwhile, the empirical likelihood ratio test is expected to be as robust as the Modified Levene's test, as the empirical likelihood ratio test is also constructed via the same distance as the Modified Levene's test. A real-life data set is used to illustrate implementation of the empirical likelihood ratio test with comparisons to the classic F-test and the Modified Levene's Test. It is confirmed that the empirical likelihood ratio test performs the best.
Author: Albert Vexler
Publisher: CRC Press
ISBN: 1351001507
Category : Mathematics
Languages : en
Pages : 149
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Book Description
Empirical Likelihood Methods in Biomedicine and Health provides a compendium of nonparametric likelihood statistical techniques in the perspective of health research applications. It includes detailed descriptions of the theoretical underpinnings of recently developed empirical likelihood-based methods. The emphasis throughout is on the application of the methods to the health sciences, with worked examples using real data. Provides a systematic overview of novel empirical likelihood techniques. Presents a good balance of theory, methods, and applications. Features detailed worked examples to illustrate the application of the methods. Includes R code for implementation. The book material is attractive and easily understandable to scientists who are new to the research area and may attract statisticians interested in learning more about advanced nonparametric topics including various modern empirical likelihood methods. The book can be used by graduate students majoring in biostatistics, or in a related field, particularly for those who are interested in nonparametric methods with direct applications in Biomedicine.
Author: Shana Leigh Carter
Publisher:
ISBN:
Category :
Languages : en
Pages : 36
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Author: Richard L. Dykstra
Publisher:
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Category : Nonparametric statistics
Languages : en
Pages : 28
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The likelihood ratio principle is employed to suggest a nonparametric test for testing equality of two distributions against a stochastic ordering alternative. The test appears to be robust against a wide range of alternatives. Percentage points for sample sizes less than or equal to twenty are provided as well as a comparison of power values for the Kolmogorov-Smirnov and Mann-Whitney-Wilcoxon tests. (Author).
Author: Charles M. Judd
Publisher: Routledge
ISBN: 1136874100
Category : Education
Languages : en
Pages : 329
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Book Description
This completely rewritten classic text features many new examples, insights and topics including mediational, categorical, and multilevel models. Substantially reorganized, this edition provides a briefer, more streamlined examination of data analysis. Noted for its model-comparison approach and unified framework based on the general linear model, the book provides readers with a greater understanding of a variety of statistical procedures. This consistent framework, including consistent vocabulary and notation, is used throughout to develop fewer but more powerful model building techniques. The authors show how all analysis of variance and multiple regression can be accomplished within this framework. The model-comparison approach provides several benefits: It strengthens the intuitive understanding of the material thereby increasing the ability to successfully analyze data in the future It provides more control in the analysis of data so that readers can apply the techniques to a broader spectrum of questions It reduces the number of statistical techniques that must be memorized It teaches readers how to become data analysts instead of statisticians. The book opens with an overview of data analysis. All the necessary concepts for statistical inference used throughout the book are introduced in Chapters 2 through 4. The remainder of the book builds on these models. Chapters 5 - 7 focus on regression analysis, followed by analysis of variance (ANOVA), mediational analyses, non-independent or correlated errors, including multilevel modeling, and outliers and error violations. The book is appreciated by all for its detailed treatment of ANOVA, multiple regression, nonindependent observations, interactive and nonlinear models of data, and its guidance for treating outliers and other problematic aspects of data analysis. Intended for advanced undergraduate or graduate courses on data analysis, statistics, and/or quantitative methods taught in psychology, education, or other behavioral and social science departments, this book also appeals to researchers who analyze data. A protected website featuring additional examples and problems with data sets, lecture notes, PowerPoint presentations, and class-tested exam questions is available to adopters. This material uses SAS but can easily be adapted to other programs. A working knowledge of basic algebra and any multiple regression program is assumed.
Author: Richard Royall
Publisher: Routledge
ISBN: 1351414550
Category : Mathematics
Languages : en
Pages : 212
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Book Description
Interpreting statistical data as evidence, Statistical Evidence: A Likelihood Paradigm focuses on the law of likelihood, fundamental to solving many of the problems associated with interpreting data in this way. Statistics has long neglected this principle, resulting in a seriously defective methodology. This book redresses the balance, explaining why science has clung to a defective methodology despite its well-known defects. After examining the strengths and weaknesses of the work of Neyman and Pearson and the Fisher paradigm, the author proposes an alternative paradigm which provides, in the law of likelihood, the explicit concept of evidence missing from the other paradigms. At the same time, this new paradigm retains the elements of objective measurement and control of the frequency of misleading results, features which made the old paradigms so important to science. The likelihood paradigm leads to statistical methods that have a compelling rationale and an elegant simplicity, no longer forcing the reader to choose between frequentist and Bayesian statistics.
Author: Junvie Montealto Pailden
Publisher:
ISBN:
Category : Analysis of means
Languages : en
Pages : 89
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Book Description
Many studies in health care deal with zero-inflated data sets characterized by a significant proportion of zero and highly skewed positive values. Although it is a common practice to use the median instead of the mean as the measure of central location in skewed data, many applications require the use of the mean. For instance, the mean can be used to recover the total medical cost which reflects the entire expenditure on health care in a given patient population. For testing the value of a mean, the empirical likelihood method offers the benefit of making no distributional assumptions beyond some mild moment conditions while retaining the same advantages that parametric likelihood based tests enjoyed. In this dissertation, we proposed an empirical likelihood ratio test for the difference between means of two zero-inflated samples. The proposed test was derived by jointly specifying the empirical likelihood for the mean parameter and the probability of taking zero value in the data. There are two unique features in this procedure. One is that the information contained in the zero observations is fully utilized and that the proposed test is insensitive to the skewness of the non-zero observations. We derive an asymptotic distribution that will be used to calibrate the statistic in testing the null hypothesis of no mean difference. We also extend the procedure to testing the mean equality of several independent zero-inflated populations. As a benchmark for comparison against conventional tests, we investigate the empirical type 1 error and power rates in finite sample settings. Both the proposed two sample test for the mean difference and the equality of means between three or more populations exhibits comparable if not superior finite sample performance. Another application of empirical likelihood approach that we consider is on detecting epidemic change point in a sequence of observations. Under some mild conditions, the asymptotic null distribution of the test statistic is showed to be an extreme distribution. Simulations indicate that the proposed test performs at par if not better than other available tests while enjoying less constraint on the data distribution.
